Transcript Sample Problem 1.1 Chemicals Why is the copper in copper wire an example of a chemical, while sunlight is not? Solution Copper is.

Sample Problem 1.1 Chemicals
Why is the copper in copper wire an example of a chemical, while sunlight is not?
Solution
Copper is a chemical that has the same composition and properties wherever it is found. Sunlight is energy
given off by the Sun. Thus, sunlight does not contain matter, which means it is not a chemical.
Study Check 1.1
Which of the following are chemicals?
a. iron
b. tin
c. a low temperature
d. water
The answers to all the Study Checks can be found at the end of this chapter.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.2 Scientific Notation
Write each of the following in scientific notation:
a. 75 000 m
b. 0.0098 g
c. 143 mL
Solution
a. To write a coefficient of 7.5, which is more than 1 but less than 10, move the decimal point four places
to the left to give 7.5  104 m.
b. To write a coefficient of 9.8, which is more than 1 but less than 10, move the decimal point three places to
the right to give 9.8  10–3g.
c. To write a coefficient of 1.43, which is more than 1 but less than 10, move the decimal point two places to
the left to give 1.43  102mL.
Study Check 1.2
Write each of the following in scientific notation:
a. 425 000 m
b. 0.000 000 86 g
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.3 Rounding Off
Round off each of the following numbers to three significant figures:
a. 35.7823 m
c. 3.8268  103 g
b. 0.002 625 L
d. 1.2836 kg
Solution
a. 35.8 m
c. 3.83  103 g
b. 0.002 63 L
d. 1.28 kg
Study Check 1.3
Round off each of the numbers in Sample Problem 1.3 to two significant figures.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.4 Significant Figures in Multiplication and
Division
Perform the following calculations of measured numbers. Give the answers with the correct number of significant
figures.
a. 56.8  0.37
b.
c.
Solution
a. 21
b. 32
c. 5.00 (add two significant zeros)
Study Check 1.4
Perform the following calculations of measured numbers and give the answers with the correct number of significant
figures:
a. 45.26  0.01088
b. 2.6  324
c.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.5 Decimal Places in Addition and Subtraction
Perform the following calculations and give the answers with the correct number of decimal places:
a. 27.8 cm + 0.235 cm
b. 153.247 g – 14.82 g
Solution
a. 28.0 cm (rounded off to one decimal place)
b. 138.43 g (rounded off to two decimal places)
Study Check 1.5
Perform the following calculations and give the answers with the correct number of decimal places:
a. 82.45 mg + 1.245 mg + 0.00056 mg
b. 4.259 L – 3.8 L
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.6 Prefixes
The storage capacity for a hard disk drive (HDD) is specified using prefixes: megabyte (MB), gigabyte (GB), or
terabyte (TB). Indicate the storage capacity in bytes for each of the following hard disk drives. Suggest a reason for
describing a HDD storage capacity in gigabytes or terabytes.
a. 5 MB
b. 2 GB
Solution
a. The prefix mega (M) in MB is equal to 1 000 000 or 1  106. Thus, 5 MB is equal to 5 000 000 (5  106) bytes.
b. The prefix giga (G) in GB is equal to 1 000 000 000 or 1  109. Thus, 2 GB is equal to 2 000 000 000
(2  109) bytes.
Expressing HDD capacity in gigabytes or terabytes gives a more reasonable number to work
with than a number with many zeros or a large power of 10
Study Check 1.6
Hard drives now have a storage capacity of 1.5 TB. How many bytes are stored?
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.7 Writing Metric Equalities
Complete the following list of metric equalities:
a. 1 L = ________ dL
b. 1 km = ________ m
c. 1 cm3 = ________ mL
Solution
a. 10 dL
b. 1  103 m
c. 1 mL
Study Check 1.7
Complete each of the following equalities:
a. 1 kg = ________ g
b. 1 mL = ________ L
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.8 Conversion Factors Stated in a Problem
Write two conversion factors for each of the following statements:
a. There are 325 mg of aspirin in 1 tablet.
b. The EPA has set the maximum level for mercury in tuna at 0.1 ppm.
Solution
a.
and
b.
and
Study Check 1.8
What conversion factors can be written for the following statements?
a. A cyclist in the Tour de France bicycle race rides at the average speed of 62.2 km/h.
b. The permissible level of arsenic in water is 10 ppb.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.9 Problem Solving Using Metric Factors
In radiological imaging such as PET or CT scans, dosages of pharmaceuticals are based on body mass. If a person
weighs 164 lb, what is the body mass in kilograms?
Solution
Step 1
State the given and needed quantities.
Given 164 lb
Need kilograms
Step 2
Write a plan to convert the given unit to the needed unit. We see that the given unit is in the
U.S. system of measurement and the needed unit in the metric system. Therefore, the
conversion factor must relate the U.S. unit lb to the metric unit kg.
Step 3
State the equalities and conversion factors needed to cancel units.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.9 Problem Solving Using Metric Factors
Continued
Solution
Step 4
Set up problem to cancel units and calculate answer. Write the given, 164 lb, and set up the
conversion factor with the unit lb in the denominator (bottom number) to cancel out the given unit
(lb) in the numerator.
Look at how the units cancel. The given unit lb cancels out and the needed unit kg is in the
numerator. The unit you want in the final answer is the one that remains after all the other units have
canceled out. This is a helpful way to check that you set up a problem properly.
The calculation gives the numerical answer, which is adjusted to give a final answer with the proper
number of significant figures (SFs).
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.9 Problem Solving Using Metric Factors
Continued
The value of 74.5 combined with the unit, kg, gives the final answer of 74.5 kg. With few
exceptions, answers to numerical problems contain a number and a unit.
Study Check 1.9
If 1890 mL of orange juice is prepared from orange juice concentrate, how many liters of orange juice is that?
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.10 Problem Solving Using Two Factors
Synthroid is used as a replacement or supplemental therapy for diminished thyroid function. A doctor’s order
prescribed a dosage of 0.200 mg. If tablets in stock contain 50 mg of Synthroid, how many tablets are required to
provide the prescribed medication?
Solution
Step 1
State the given and needed quantities.
Given 0.200 mg of Synthroid
Need number of tablets
Step 2
Write a plan to convert the given unit to the needed unit.
Step 3
State the equalities and conversion factors needed to cancel units. In the problem, the
information for the dosage is given as 50 mg per tablet. Using this as an equality along with the
metric equality for milligrams and micrograms provides the following conversion factors:
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.10 Problem Solving Using Two Factors
Continued
Solution
Step 4
Set up problem to cancel units and calculate answer. The problem can be set up using the
metric factor to cancel milligrams, and then the clinical factor to obtain tablets as the final unit.
Study Check 1.10
One medium bran muffin contains 4.2 g of fiber. How many ounces (oz) of fiber are obtained by eating three
medium bran muffins if 1 lb = 16 oz?
(Hint: number of muffins
g of fiber
lb
oz)
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.11 Using a Percent as a Conversion Factor
A person who exercises regularly has 16% body fat. If this person weighs 155 lb, what is the mass, in kilograms, of
body fat?
Solution
Step 1
State the given and needed quantities.
Given 155 lb of body weight; 16% body fat
Need kilograms of body fat
Step 2
Write a plan to convert the given unit to the needed unit.
Step 3
State the equalities and conversion factors needed to cancel units. One equality is the U.S.–
metric factor for lb and kg. The second is the percent factor derived from the percentage
information given in the problem.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.11 Using a Percent as a Conversion Factor
Continued
Solution
Step 4
Set up problem to cancel units and calculate answer. We can set up the problem using
conversion factors to cancel each unit, starting with lb of body weight, until we obtain the final unit,
kg of body fat, in the numerator. After we count the significant figures in the measured quantities,
we write the needed answer with the proper number of significant figures.
Study Check 1.11
Uncooked lean ground beef can contain up to 22% fat by mass. How many grams of fat would be contained in
0.25 lb of the ground beef?
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.12 Calculating Density
High-density lipoprotein (HDL) contains large amounts of proteins and small amounts of cholesterol. If a 0.258-g
sample of HDL has a volume of 0.215 cm3, what is the density of the HDL sample?
Solution
Step 1
State the given and needed quantities.
Given mass of HDL sample = 0.258 g; volume = 0.215 cm3
Need density (g/cm3)
Step 2
Write the density expression.
Step 3
Express mass in grams and volume in milliliters (mL) or cm3.
Mass of HDL sample = 0.258 g
Volume of HDL sample = 0.215 cm3
Substitute mass and volume into the density expression and calculate the density.
Step 4
Study Check 1.12
Low-density lipoprotein (LDL) contains small amounts of proteins and large amounts of cholesterol. If a
0.380-g sample of LDL has a volume of 0.362 cm3, what is the density of the LDL sample?
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.13 Using Volume Displacement to Calculate
Density
A lead weight used in the belt of a scuba diver has a mass of 226 g. When the lead weight is placed in a graduated
cylinder containing 200.0 mL of water, the water level rises to 220.0 mL. What is the density of the lead weight
(g/mL)?
Solution
Step 1
State the given and needed quantities.
Given mass = 226 g; water level before object submerged = 200.0 mL; water level after object
submerged = 220.0 mL
Need density (g/mL)
Step 2
Write the density expression.
Step 3
Express mass in grams and volume in milliliters (mL) or cm3.
Mass of lead weight = 226 g
The volume of the lead weight is equal to the volume of water displaced, which is calculated as
follows:
Water level after object submerged
= 220.0 mL
Water level before object submerged
= -200.0 mL
Water displaced (volume of lead weight) = 20.0 mL
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.13 Using Volume Displacement to Calculate
Density
Continued
Solution
Step 4
Substitute mass and volume into the density expression and calculate the density. The density
is calculated by dividing the mass (g) by the volume (mL). Be sure to use the volume of water the
object displaced and not the original volume of water.
Study Check 1.13
A total of 0.50 lb of glass marbles is added to 425 mL of water. The water level rises to a volume of 528 mL.
What is the density (g/mL) of the glass marbles?
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.14 Problem Solving with Density
John took 2.0 teaspoons (tsp) of cough syrup for a persistent cough. If the syrup had a density of 1.20 g/mL and
there is 5.0 mL in 1 tsp, what was the mass, in grams, of the cough syrup?
Solution
Step 1
State the given and needed quantities.
Given 2.0 tsp
Need grams of syrup
Step 2
Write a plan to calculate the needed quantity.
Step 3
Write equalities and their conversion factors including density.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.
Sample Problem 1.14 Problem Solving with Density
Continued
Solution
Step 4
Set up problem to calculate the needed quantity.
Study Check 1.14
How many milliliters of mercury are in a thermometer that contains 20.4 g of mercury? (See Table 1.13 for
the density of mercury.)
Chemistry: An Introduction to General, Organic, and Biological Chemistry, 11th Edition
Karen C. Timberlake
© 2012 Pearson Education, Inc.